3/4x+1/2=1/2x-4

Solution for 3/4x+1/2=1/2x-4 equation:

3/4x+1/2=1/2x-4

We move all terms to the left:

3/4x+1/2-(1/2x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

3/4x-1/2x+4+1/2=0

We calculate fractions


24x/32x^2+(-4x)/32x^2+4x/32x^2+4=0

We multiply all the terms by the denominator


24x+(-4x)+4x+4*32x^2=0

We add all the numbers together, and all the variables

28x+(-4x)+4*32x^2=0

Wy multiply elements

128x^2+28x+(-4x)=0

We get rid of parentheses

128x^2+28x-4x=0

We add all the numbers together, and all the variables

128x^2+24x=0

a = 128; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·128·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*128}=\frac{-48}{256}
=-3/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*128}=\frac{0}{256}
=0
$